Hopfield model is known as a representative neural network that has mutually connected nodes. This model is structured, as in FIG. 16, by inputting the outputs for each of multiple parallel neurons as inputs for every other neuron excepting that of itself.
Defining the output of i-th neuron as "x.sub.i ", the coupling weight of synapses of output of i-th neuron as "w.sub.ij ", and the threshold of i-th neuron as ".theta..sub.i ", the energy "E" of neural network of Hopfield can be expressed by the formula (1) when the coupling weight of synapses is symmetry (w.sub.ij =w.sub.ji). EQU E=-( 1/2).SIGMA.w.sub.ij x.sub.i x.sub.j -.SIGMA..theta..sub.i x.sub.i +G(1 )
Here, "G" is an item of integral calculus representing an inverse function of a cost function ("F"; G=1/F). It is "0" in a dispersed model in which the output of a neuron is either "0" or "1".
In this specification, "cost" means the result obtained through the predetermined function performed on the solutions of adaptation problems. It is used with the meanings of not only the economical expense but also the sense including the conception of risk, time, etc. for the base of evaluation of a problem to be solved.
When an adaptation problem is solved using a neural network of Hopefield type, the following steps are executed: i) setting cost function "F" for solving an adaptation problem; ii) coupling weight "wij" is determined for all neurons according to the cost function "F" so that energy "E" is coincident with cost function "F"; and iii) the initial value is given to each neuron and the neural network begins working.
The neural network given a random initial value repeats Markov transition through the Monte Carlo method. The solution of the adaptation problem is obtained when the output of each neuron is stabilized and converged by repeating the predetermined number of transitions.